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Activity 2 Direction: Solve the following problems completely (5 points each); 1. If there are 7 distinct points on a plane with no three of which are collinear, how many different polygons can be possibly formed? In a 10-item Mathematics problem solving test, how many ways can you select 5 problems to solve? 3. How many different sets of 5 cards each can be formed from a standard deck of 52 cards? 2. a​

Sagot :

Answer:

99polygons

2598960 sets

252 ways

Step-by-step explanation:

2. 7C3=35 , 7C4=35 ,7C5= 21, 7C6=7 , 7C7=1

Add the answer from 7C3 to 7C7 = 35+35+21+7+1 = 99 polygons

3. The 1st choice is 1 of 52.

Then 1 of 51, etc.

--> 52×51×50×49×48 = 311857200

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But, choosing cards A,B,C,D & E is the same as B,A,D,E & C.

= 120 (5×4×3×2×1) ways to get the same 5 cards.

311857200/120 = 2598960 sets

4. We have 5 items to choose from 10 possible problems, so r = 5, n = 10. Substituting it to the formula and simplifying gives us:

= 10!/5!(10-5)!

=10!/5!5!

=10×9×8×7×6×5!/5×4×3×2×1×5!

=3×2×7×6

=252 ways